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Integrated production-inventory model for multi-item raw materials with exponential quality degradation: a real case study

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Abstract

Inventory issues involving quality degradation are complex to resolve and harm company performance. This study proposes an integrated production-inventory model for multi-item raw materials with exponential quality degradation. The proposed model is based on a finished product that requires several materials that degrade quality in the food industry. The proposed model’s objective function is to maximize profits using the decision variables and an optimal number of raw material shipments (\({m}_{j}\)), production time cycle (\(T\)), and the number of finished product shipments (\(n\)). The grey wolf optimizer (GWO) algorithm is proposed in this study to solve this problem. A case study was conducted on the Indonesian food industry, which produces a finished product from five raw materials. The results demonstrated that the proposed GWO algorithm could solve the production-inventory model problem. A sensitivity analysis of the research is also presented to investigate the impact of changes in the variable rate of quality degradation (\(k\)), rate of production (\(P\)), and demand (\(D\)).

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  1. Department of Industrial Engineering, Universitas Muhammadiyah Malang, Malang, Indonesia

    Dana Marsetiya Utama, Fakhrina Fahma Abdullah, Ikhlasul Amallynda & Teguh Baroto

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DMU: Conceptualization Model, Methodology, Data curation, Calculation, Writing-Original draft preparation, and Revision. FFA: Conceptualization, Writing- Reviewing, Revision and Editing, Supervision. IA: Conceptualization Model and Methodology. TB: Conceptualization Model and Methodology.

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Appendix A

Appendix A

This section presents the calculation of the average inventory of finished products and each material. Based on the optimization results with the GWO algorithm, the optimal decision for the production cycle (T) is 0.7273, and the frequency of finished product delivery (n) is once. Meanwhile, the delivery of raw materials 1–5 (\({{\varvec{m}}}_{1}-{{\varvec{m}}}_{5}\)) are 10, 4, 6, 1, and 1, respectively. The formula for the average inventory of finished products is presented in Eq. (20).

$$I_{1} = \frac{DT}{{2n}}\left( {\frac{D}{P}\left( {2 - n} \right) + \left( {n - 1} \right)} \right)$$
(20)

Based on this formula, the average finished product inventory is as follows:

$$I_{1} = \frac{{7020{*}0.7273}}{2*1}\left( {\frac{7020}{{7500}}\left( {2 - 1} \right) + \left( {1 - 1} \right)} \right) = 2,389,4$$

It shows that the average inventory of finished products is 2,389.4 product units. Meanwhile, the formula for the average inventory of each raw material is presented in Eq. (21).

$$I_{{0_{j} }} = \frac{{\lambda_{j} D^{2} T}}{{2m_{j} \lambda_{j} P}}$$
(21)

Based on this formula, the average inventory of each raw material is as follows:

$$I_{{0_{1} }} = \frac{{0.293*7020^{2} *0.7273}}{2*10*0.293*7500} = 238.94$$
$$I_{{0_{2} }} = \frac{{0.43*7020^{2} *0.7273}}{2*4*0.43*7500} = 597.36$$
$$I_{{0_{3} }} = \frac{{0.004*7020^{2} *0.7273}}{2*6*0.004*7500} = { 398}.{24}$$
$$I_{{0_{4} }} = \frac{{32*7020^{2} *0.7273}}{2*1*32*7500} = { 2389}.{44}$$
$$I_{{0_{5} }} = \frac{{1*7020^{2} *0.7273}}{2*1*1*7500} = 2389.44$$

These results show that the average inventory of each raw material 1 to 5 is 238.94, 597.36, 398.24, 2389.44, and 2389.44, respectively.

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Utama, D.M., Abdullah, F.F., Amallynda, I. et al. Integrated production-inventory model for multi-item raw materials with exponential quality degradation: a real case study. OPSEARCH (2024). https://doi.org/10.1007/s12597-024-00759-z

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